Matrices for graphs designs and codes

Abstract

The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.

abstract = "The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.",

author = "W.H. Haemers",

note = "Pagination: 460",

year = "2011",

language = "English",

isbn = "9781607506638",

series = "NATO Science for Peace and Security Series - D: Information and Communication Security",

N2 - The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.

AB - The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.